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12/5/2013 10:44:25 PM
9
Hi. Calculus Tutor here. I'm a little rusty on the entire Lagrangian thing as it's been a while since I took multi-variable calculus and we don't get a ton of multi-variable students in the tutoring center, but I'll see what I can do.
English
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Well, it's a physics question, but I'll take all the help I can get. I just need to find the equation of constraint as a function of Theta and Phi for a smaller cylinder rotating around a larger cylinder where Theta is the angle from the vertical at the center of the large cylinder to the center of the smaller cylinder and Phi is the angular rotation of the small cylinder (where d/dt(Phi) is conventionally called w (omega)). I've got the rest down pretty well.
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Are these Cylinders parallel or perpendicular?
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Ah, the axis are parallel. My apologies. And both are perpendicular to gravity, but that has nothing to do with the constraint function.
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So if I'm understanding this properly, you have like a small cylinder rolling around the edge of a larger cylinder at some fixed radius equal to bothy cylinder's radiuses combined. The constraint then is trying to describe the possible locations that this can could be rotating at? It seems like your constraint wouldn't contain phi, as there's nothing stopping the small cylinder from rotating fully around the large cylinder right? In which case, it seems like the constraint would be something like "Theta can't be large enough to the point where the can is no longer in contact with the other can?" It's a little hard to picture.
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You have the idea right, yes. The large radius is a, and the small radius is x*a, where x<1.
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So yeah, like I said, your constraint would most like revolve around your theta.
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Except the function has to be equal to a constant. My intent was to find some way to relate theta and phi to the two radii.
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Doesn't seem likely if I understand this correctly. The radius between the two cylinders are going to be constant, yes, but unrelated to either Theta (pictured in the picture) or Phi (which from my understanding was where the other cylinder was rotating around the object). You might want to ask your teacher / professor on this one unless I've gotten something worng, sorry :|
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Tilt the picture on the side, and you've got it. :P But thanks for trying to help, anyway. I can't blame you for not getting it, as I most certainly don't, even though I've been able to routinely do similar problems of this type.
